Skip to main content
Log in

An estimate of approximation constants for p-adic and real varieties

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Arjunwadkar, H. and Moh, T.T.:On the approximations of hypersurfaces Preprint

  2. Arnol'd, V.I.:Critical points of smooth functions and their normal forms. Russian Math. Surveys, 30:5, 1975

    Article  Google Scholar 

  3. Arnol'd, V.I., Varchenko, A., Goussein-Zadé, S.:Singularités des applications différentiables. (en deux parties). Editions MIR, Moscou, 1986

    Google Scholar 

  4. Artin, M.:Algebraic approximation of structures over complete local rings. Publications Mathématiques Institut des Hautes études Scientifiques, 36, 23–58, 1969

    MATH  MathSciNet  Google Scholar 

  5. Becker, J., Denef, J., Lipshitz, L., van den Dries, L.:Ultraproducts and Approximation in Local Rings I. Inventiones Mathematicae. 51, 189–203, 1979

    Article  MATH  MathSciNet  Google Scholar 

  6. Berger, M.:géométrie: convexes et polytopes, polyèdres réguliers, aires et volumes. Cedic, Fernand Nathan, 1978

  7. Birch, B.J., Mc Cann, K.:A criterion for the p-adic solubility of Diophantine equations. Quart. J. Math., Oxford (2), 1–23, 1984

    Google Scholar 

  8. Bochnak, J., Risler, J.J.:Sur les exposants de Łojasiewicz. Comment. Math. Helv. 50, 493–507, 1975

    Article  MATH  MathSciNet  Google Scholar 

  9. Bollaerts, D.:Thesis. April 1988, K.U.-Leuven

  10. Bröcker, T., Jänich, K.:Einführung in die Differentialtopologie. Springer Verlag, Berlin, 1973

    MATH  Google Scholar 

  11. Brownawell, D.:Bounds for the degrees in the Nullstellensatz. Annals of Mathematics, 126, 577–591 1987

    Article  MathSciNet  Google Scholar 

  12. Denef, J.:The rationality of the Poincaré series associated to the p-adic points on a variety. Inventiones Mathematicae, 77, 1–23, 1984

    Article  MATH  MathSciNet  Google Scholar 

  13. Denef, J.:Poles of p-adic complex powers and Newton polyhedra. Groupe d'étude d'Analyse ultramétrique, 12-e année, n. 17, 1984–1985

  14. Denef, J.:Handwritten notes

  15. Denef, J.:Poles of p-adic complex powers and Newton polyhedra. Preprint

  16. Denef, J. and Sargos P.:Polyèdres de Newton et distributions f 3. In preparation

  17. Denef, J. and van den Dries, L.:P-adic and real subanalytic sets. Preprint. To appear in Annals of Mathematics

  18. Ehlers, F.:Newton polyheder und die Monodromie von Hyperflächensingularitäten. Bonner Mathematische Schriften, Bonn, 1973

  19. Greenberg, M.:Rational points in henselian discrete valuation rings. Publ. Math. Inst. Hautes Etudes Sci., n. 23, 1964

  20. Hironaka, H.:Introduction to real-analytic sets and real-analytic maps. Instituto matematico L. Tonelli, Pisa, 1973

    Google Scholar 

  21. Hörmander, L.:On the division of distribution of polynomials. Arkiv för Mathematik, band 3, n. 53, 1958

  22. Khovanskii, A.G.:Newton polyhedra (resolution of singularities). Journal of Soviet Mathematics, 27, 1984

  23. Khovanskii, A.G.:Newton polyhedra and toroidal singularities. Functional Analysis and its Applications, 11, 289–295, 1977

    Article  Google Scholar 

  24. Kneser, M.:Konstruktive Lösung p-adischer Gleichungssystemen. Göttinger Mathematische Nachrichten, 1979

  25. Kouchnirenko A.G.:Polyhèdres de Newton et nombres de Milnor. Inventiones Mathematicae, 417–429, 1981

  26. Kuo T.-C.:Computation of Łojasiewicz exponents and Newton polygons. Mathematica Helvetica, 1974

  27. Lichtin, B.:Estimation of Łojasiewicz exponents and Newton polygons. Inventiones Mathematicae, 417–429, 1981

  28. Lichtin, B. and Meuser, D.:Poles of a complex zeta function and Newton polyhedra. Compositio Mathematica, 55, 313–332, 1985.

    MATH  MathSciNet  Google Scholar 

  29. Łojasiewicz, S.:Ensembles sémianalytiques. I.H.E.S. Bures-Sur-Yvette, 1965

    Google Scholar 

  30. Malgrange, B.:Division des Distributions. Séminaire Bourbaki, 12-e année, n. 203, 1959/60

  31. Milnor, J.:Singular points of complex hypersurfaces. Princeton University Press, 1968

  32. Mc Mullan, P.C. and Shephard, C.G.:Convex polytopes and the upper bound conjecture. London Mathematical Society, Lecture Note series number 3, Cambridge, 1971

  33. Preparata, F.:Computational geometry. Springer Verlag, 1986

  34. Sargos, P.:Thèse Docteur d'état es sciences. Université de Bordeaux, 1987

  35. Schappacher, N.:Ph-D thesis. Göttingen, 1978

  36. Schappacher, N.:L'inégalité de Łojasiewicz ultramétrique. C.R. Acad. Sc. Paris 296, 439–442, 1983

    MATH  MathSciNet  Google Scholar 

  37. Schappacher, N.:Some remarks on a theorem of M.J. Greenberg. Proceedings of the 1979 Kingston Number Theory conference. Queens's Mathematical papers, 100–114, 1980

  38. Schwartz, L.:Théorie des distributions, Paris, Hermann 1966

    MATH  Google Scholar 

  39. Varcenko, A.N.:Newton polyhedra and estimations of oscillatory integrals. Functional Anal. and its Appl., 10, 175–196, 1977

    Article  Google Scholar 

  40. Varcenko, A.N.:Zetafunction of monodromy and Newton's diagram. Inventiones Mathematicae, 37, 235–262, 1976

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bollaerts, D. An estimate of approximation constants for p-adic and real varieties. Manuscripta Math 69, 411–442 (1990). https://doi.org/10.1007/BF02567935

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02567935

Keywords

Navigation